The Collaborative International Dictionary of English v.0.48:

Annats \An"nats\, Annates \An"nates\, n. pl. [See Ann.] (Eccl.
   Law)
   The first year's profits of a spiritual preferment, anciently
   paid by the clergy to the pope; first fruits. In England,
   they now form a fund for the augmentation of poor livings.
   [1913 Webster]